Soliton type phenomena in discrete systems

As an example of discrete soliton-type systems, the Ablowitz-Ladik (AL) sys tem as a numerical scheme for the cubic nonlinear Schrodinger (NLS) is cons idered. Among numerous numerical schemes for the NLS equation, the AL schem e is an exceptional one since it is completely integrable. This means that it has multisoliton and multiphase quasi-periodic solutions, the dispersion relations of a similar form and also an infinite set of conserved quantiti es. Due to these close affinities, the AL-system can be exploited as a part icularly convenient numerical algorithm for the NLS system. A similar concl usion relates also to the other soliton-type equations, e.g., to the sine-G ordon equation and its specific discrete counterpart. (C) 1999 Elsevier Sci ence B.V. All rights reserved.